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<div class="header">
  <div class="summary">
<a href="classEigen_1_1Transform-members.html">List of all members</a> &#124;
<a href="#pub-types">Public Types</a> &#124;
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pub-static-methods">Static Public Member Functions</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::Transform&lt; Scalar_, Dim_, Mode_, Options_ &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__Geometry__chapter.html">Geometry</a> &raquo; <a class="el" href="group__Geometry__Reference.html">Reference</a> &raquo; <a class="el" href="group__Geometry__Module.html">Geometry module</a></div></div>  </div>
</div><!--header-->
<div class="contents">
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename Scalar_, int Dim_, int Mode_, int Options_&gt;<br />
class Eigen::Transform&lt; Scalar_, Dim_, Mode_, Options_ &gt;</h3>

<p>Represents an homogeneous transformation in a N dimensional space. </p>
<p>This is defined in the Geometry module.</p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/Geometry&gt;</span> </div>
</div><!-- fragment --><dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">Scalar_</td><td>the scalar type, i.e., the type of the coefficients </td></tr>
    <tr><td class="paramname">Dim_</td><td>the dimension of the space </td></tr>
    <tr><td class="paramname">Mode_</td><td>the type of the transformation. Can be:<ul>
<li><a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a0872f0a82453aaae40339c33acbb31fb">Affine</a>: the transformation is stored as a (Dim+1)^2 matrix, where the last row is assumed to be [0 ... 0 1].</li>
<li><a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>: the transformation is stored as a (Dim)x(Dim+1) matrix.</li>
<li><a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a0f7338b8672884554e8642bce9e44183">Projective</a>: the transformation is stored as a (Dim+1)^2 matrix without any assumption.</li>
<li><a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a84413028615d2d718bafd2dfb93dafef">Isometry</a>: same as <a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a0872f0a82453aaae40339c33acbb31fb">Affine</a> with the additional assumption that the linear part represents a rotation. This assumption is exploited to speed up some functions such as <a class="el" href="classEigen_1_1Transform.html#ab8dbcd157bf194efca1a5413c0945211">inverse()</a> and <a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation()</a>. </li>
</ul>
</td></tr>
    <tr><td class="paramname">Options_</td><td>has the same meaning as in class <a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors.">Matrix</a>. It allows to specify DontAlign and/or RowMajor. These Options are passed directly to the underlying matrix type.</td></tr>
  </table>
  </dd>
</dl>
<p>The homography is internally represented and stored by a matrix which is available through the <a class="el" href="classEigen_1_1Transform.html#a50338fe8ce60e175fa5a42046ea70ed0">matrix()</a> method. To understand the behavior of this class you have to think a <a class="el" href="classEigen_1_1Transform.html" title="Represents an homogeneous transformation in a N dimensional space.">Transform</a> object as its internal matrix representation. The chosen convention is right multiply:</p>
<div class="fragment"><div class="line">v<span class="stringliteral">&#39; = T * v </span></div>
</div><!-- fragment --><p>Therefore, an affine transformation matrix M is shaped like this:</p>
<p>\( \left( \begin{array}{cc} linear &amp; translation\\ 0 ... 0 &amp; 1 \end{array} \right) \)</p>
<p>Note that for a projective transformation the last row can be anything, and then the interpretation of different parts might be slightly different.</p>
<p>However, unlike a plain matrix, the <a class="el" href="classEigen_1_1Transform.html" title="Represents an homogeneous transformation in a N dimensional space.">Transform</a> class provides many features simplifying both its assembly and usage. In particular, it can be composed with any other transformations (<a class="el" href="classEigen_1_1Transform.html" title="Represents an homogeneous transformation in a N dimensional space.">Transform</a>,<a class="el" href="classEigen_1_1Translation.html" title="Represents a translation transformation.">Translation</a>,<a class="el" href="classEigen_1_1RotationBase.html" title="Common base class for compact rotation representations.">RotationBase</a>,<a class="el" href="classEigen_1_1DiagonalMatrix.html" title="Represents a diagonal matrix with its storage.">DiagonalMatrix</a>) and can be directly used to transform implicit homogeneous vectors. All these operations are handled via the operator*. For the composition of transformations, its principle consists to first convert the right/left hand sides of the product to a compatible (Dim+1)^2 matrix and then perform a pure matrix product. Of course, internally, operator* tries to perform the minimal number of operations according to the nature of each terms. Likewise, when applying the transform to points, the latters are automatically promoted to homogeneous vectors before doing the matrix product. The conventions to homogeneous representations are performed as follow:</p>
<p><b><a class="el" href="classEigen_1_1Translation.html" title="Represents a translation transformation.">Translation</a></b> t (Dim)x(1): \( \left( \begin{array}{cc} I &amp; t \\ 0\,...\,0 &amp; 1 \end{array} \right) \)</p>
<p><b>Rotation</b> R (Dim)x(Dim): \( \left( \begin{array}{cc} R &amp; 0\\ 0\,...\,0 &amp; 1 \end{array} \right) \)</p>
<p><b>Scaling</b> <b><a class="el" href="classEigen_1_1DiagonalMatrix.html" title="Represents a diagonal matrix with its storage.">DiagonalMatrix</a></b> S (Dim)x(Dim): \( \left( \begin{array}{cc} S &amp; 0\\ 0\,...\,0 &amp; 1 \end{array} \right) \)</p>
<p><b>Column</b> <b>point</b> v (Dim)x(1): \( \left( \begin{array}{c} v\\ 1 \end{array} \right) \)</p>
<p><b>Set</b> <b>of</b> <b>column</b> <b>points</b> V1...Vn (Dim)x(n): \( \left( \begin{array}{ccc} v_1 &amp; ... &amp; v_n\\ 1 &amp; ... &amp; 1 \end{array} \right) \)</p>
<p>The concatenation of a <a class="el" href="classEigen_1_1Transform.html" title="Represents an homogeneous transformation in a N dimensional space.">Transform</a> object with any kind of other transformation always returns a <a class="el" href="classEigen_1_1Transform.html" title="Represents an homogeneous transformation in a N dimensional space.">Transform</a> object.</p>
<p>A little exception to the "as pure matrix product" rule is the case of the transformation of non homogeneous vectors by an affine transformation. In that case the last matrix row can be ignored, and the product returns non homogeneous vectors.</p>
<p>Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation, it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix. The solution is either to use a Dim x Dynamic matrix or explicitly request a vector transformation by making the vector homogeneous: </p><div class="fragment"><div class="line">m<span class="stringliteral">&#39; = T * m.colwise().homogeneous();</span></div>
</div><!-- fragment --><p> Note that there is zero overhead.</p>
<p>Conversion methods from/to Qt's QMatrix and QTransform are available if the preprocessor token EIGEN_QT_SUPPORT is defined.</p>
<p>This class can be extended with the help of the plugin mechanism described on the page <a class="el" href="TopicCustomizing_Plugins.html">Extending MatrixBase (and other classes)</a> by defining the preprocessor symbol <code>EIGEN_TRANSFORM_PLUGIN</code>.</p>
<dl class="section see"><dt>See also</dt><dd>class <a class="el" href="classEigen_1_1Matrix.html" title="The matrix class, also used for vectors and row-vectors.">Matrix</a>, class <a class="el" href="classEigen_1_1Quaternion.html" title="The quaternion class used to represent 3D orientations and rotations.">Quaternion</a> </dd></dl>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:aa4d22f6827bf7c2b67d0c609c8e31fdb"><td class="memItemLeft" align="right" valign="top">typedef std::conditional_t&lt; int(Mode)==int(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>), <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a> &amp;, <a class="el" href="classEigen_1_1Block.html">Block</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>, Dim, HDim &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#aa4d22f6827bf7c2b67d0c609c8e31fdb">AffinePart</a></td></tr>
<tr class="separator:aa4d22f6827bf7c2b67d0c609c8e31fdb"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0919aff2b16c0c97cbfa4dd16a71c946"><td class="memItemLeft" align="right" valign="top">typedef std::conditional_t&lt; int(Mode)==int(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>), const <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a> &amp;, const <a class="el" href="classEigen_1_1Block.html">Block</a>&lt; const <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>, Dim, HDim &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a0919aff2b16c0c97cbfa4dd16a71c946">ConstAffinePart</a></td></tr>
<tr class="separator:a0919aff2b16c0c97cbfa4dd16a71c946"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9ebace9975ee01a2b82f63ee353a549a"><td class="memItemLeft" align="right" valign="top">typedef const <a class="el" href="classEigen_1_1Block.html">Block</a>&lt; <a class="el" href="classEigen_1_1Transform.html#ada1f35e4ec62a77c63c99282f95cbbc8">ConstMatrixType</a>, Dim, Dim, int(Mode)==(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>) &amp;&amp;(int(Options)&amp;<a class="el" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>)==0 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a9ebace9975ee01a2b82f63ee353a549a">ConstLinearPart</a></td></tr>
<tr class="separator:a9ebace9975ee01a2b82f63ee353a549a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ada1f35e4ec62a77c63c99282f95cbbc8"><td class="memItemLeft" align="right" valign="top">typedef const <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ada1f35e4ec62a77c63c99282f95cbbc8">ConstMatrixType</a></td></tr>
<tr class="separator:ada1f35e4ec62a77c63c99282f95cbbc8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae0f9a88eecc888dbffb8b27f67d2e540"><td class="memItemLeft" align="right" valign="top">typedef const <a class="el" href="classEigen_1_1Block.html">Block</a>&lt; <a class="el" href="classEigen_1_1Transform.html#ada1f35e4ec62a77c63c99282f95cbbc8">ConstMatrixType</a>, Dim, 1,!(internal::traits&lt; <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a> &gt;::Flags &amp;<a class="el" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a>)&gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ae0f9a88eecc888dbffb8b27f67d2e540">ConstTranslationPart</a></td></tr>
<tr class="separator:ae0f9a88eecc888dbffb8b27f67d2e540"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae5001c5914013c18924faa92590251f6"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ae5001c5914013c18924faa92590251f6">Index</a></td></tr>
<tr class="separator:ae5001c5914013c18924faa92590251f6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae14a5178e9c3b434b6ab343bba8a9232"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Dim, Options &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ae14a5178e9c3b434b6ab343bba8a9232">LinearMatrixType</a></td></tr>
<tr class="separator:ae14a5178e9c3b434b6ab343bba8a9232"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad6d84e2c0438b13fc4fff332aca116fa"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Block.html">Block</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>, Dim, Dim, int(Mode)==(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>) &amp;&amp;(int(Options)&amp;<a class="el" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>)==0 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ad6d84e2c0438b13fc4fff332aca116fa">LinearPart</a></td></tr>
<tr class="separator:ad6d84e2c0438b13fc4fff332aca116fa"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2c59f34fa172d9781f1bdd18d83e6c23"><td class="memItemLeft" align="right" valign="top">typedef internal::make_proper_matrix_type&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Rows, HDim, Options &gt;::type&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a></td></tr>
<tr class="separator:a2c59f34fa172d9781f1bdd18d83e6c23"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a37f6f58b51298ca64c6cf8457a73538d"><td class="memItemLeft" align="right" valign="top">typedef Scalar_&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a></td></tr>
<tr class="separator:a37f6f58b51298ca64c6cf8457a73538d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8a56c160574e9f4da03c987a12eefb68"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, TransformTimeDiagonalMode &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a8a56c160574e9f4da03c987a12eefb68">TransformTimeDiagonalReturnType</a></td></tr>
<tr class="separator:a8a56c160574e9f4da03c987a12eefb68"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a98ad9f68ecea39c6f0b5fcf184fbcb47"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Block.html">Block</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>, Dim, 1,!(internal::traits&lt; <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a> &gt;::Flags &amp;<a class="el" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a>)&gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a98ad9f68ecea39c6f0b5fcf184fbcb47">TranslationPart</a></td></tr>
<tr class="separator:a98ad9f68ecea39c6f0b5fcf184fbcb47"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af0ce638b81842cd4622f67d5ab655b2e"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Translation.html">Translation</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#af0ce638b81842cd4622f67d5ab655b2e">TranslationType</a></td></tr>
<tr class="separator:af0ce638b81842cd4622f67d5ab655b2e"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7b27e078095260aebef444023b96d090"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, 1 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a7b27e078095260aebef444023b96d090">VectorType</a></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a61b7a97da2ce3e46902d97af27c1a79a"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#aa4d22f6827bf7c2b67d0c609c8e31fdb">AffinePart</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a61b7a97da2ce3e46902d97af27c1a79a">affine</a> ()</td></tr>
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<tr class="memitem:a084060033661f673a7a05eb9b28d1584"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#a0919aff2b16c0c97cbfa4dd16a71c946">ConstAffinePart</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a084060033661f673a7a05eb9b28d1584">affine</a> () const</td></tr>
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<tr class="memitem:a3ed6d91135a87d168d5470a51f1dbb3b"><td class="memTemplParams" colspan="2">template&lt;typename NewScalarType &gt; </td></tr>
<tr class="memitem:a3ed6d91135a87d168d5470a51f1dbb3b"><td class="memTemplItemLeft" align="right" valign="top">internal::cast_return_type&lt; <a class="el" href="classEigen_1_1Transform.html">Transform</a>, <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; NewScalarType, Dim, Mode, Options &gt; &gt;::type&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a3ed6d91135a87d168d5470a51f1dbb3b">cast</a> () const</td></tr>
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<tr class="memitem:a7213fd78501c1185c4a1441e33c812d3"><td class="memTemplParams" colspan="2">template&lt;typename RotationMatrixType , typename ScalingMatrixType &gt; </td></tr>
<tr class="memitem:a7213fd78501c1185c4a1441e33c812d3"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a7213fd78501c1185c4a1441e33c812d3">computeRotationScaling</a> (RotationMatrixType *<a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation</a>, ScalingMatrixType *scaling) const</td></tr>
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<tr class="memitem:a247b079c63f46bb652b3776484838216"><td class="memTemplParams" colspan="2">template&lt;typename ScalingMatrixType , typename RotationMatrixType &gt; </td></tr>
<tr class="memitem:a247b079c63f46bb652b3776484838216"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a247b079c63f46bb652b3776484838216">computeScalingRotation</a> (ScalingMatrixType *scaling, RotationMatrixType *<a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation</a>) const</td></tr>
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<tr class="memitem:a01b957a1a2779b30c7756c7ccc74fdb3"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a01b957a1a2779b30c7756c7ccc74fdb3">data</a> ()</td></tr>
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<tr class="memitem:acafc06db5d5cc36e316a5d85d5fa7bc8"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> *&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#acafc06db5d5cc36e316a5d85d5fa7bc8">data</a> () const</td></tr>
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<tr class="memitem:a7924a893752f42d33ca8dca33280ebc7"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a7924a893752f42d33ca8dca33280ebc7">EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE</a> (Scalar_, Dim_==<a class="el" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="el" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> :(Dim_+1) *(Dim_+1)) enum</td></tr>
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<tr class="memitem:a4fbbe0434e3093ec44287f45f27b66e3"><td class="memTemplParams" colspan="2">template&lt;typename PositionDerived , typename OrientationType , typename ScaleDerived &gt; </td></tr>
<tr class="memitem:a4fbbe0434e3093ec44287f45f27b66e3"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Mode, Options &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a4fbbe0434e3093ec44287f45f27b66e3">fromPositionOrientationScale</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; PositionDerived &gt; &amp;position, const OrientationType &amp;orientation, const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; ScaleDerived &gt; &amp;scale)</td></tr>
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<tr class="memitem:ab8dbcd157bf194efca1a5413c0945211"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ab8dbcd157bf194efca1a5413c0945211">inverse</a> (<a class="el" href="group__enums.html#gaee59a86102f150923b0cac6d4ff05107">TransformTraits</a> traits=(<a class="el" href="group__enums.html#gaee59a86102f150923b0cac6d4ff05107">TransformTraits</a>) Mode) const</td></tr>
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<tr class="memitem:a5ca48af274337349e9b8d129ecf7c35b"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a5ca48af274337349e9b8d129ecf7c35b">isApprox</a> (const <a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;other, const typename <a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &gt;::Real &amp;prec=<a class="el" href="structEigen_1_1NumTraits.html">NumTraits</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &gt;::dummy_precision()) const</td></tr>
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<tr class="memitem:a8aafb7e536e68b13b05a5cbd24d71379"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#ad6d84e2c0438b13fc4fff332aca116fa">LinearPart</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a8aafb7e536e68b13b05a5cbd24d71379">linear</a> ()</td></tr>
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<tr class="memitem:a10681d9bbc6a7a81a9111b1f9e186948"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#a9ebace9975ee01a2b82f63ee353a549a">ConstLinearPart</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a10681d9bbc6a7a81a9111b1f9e186948">linear</a> () const</td></tr>
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<tr class="memitem:adb282510aef3951e1deb27466cf8167b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#adb282510aef3951e1deb27466cf8167b">makeAffine</a> ()</td></tr>
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<tr class="memitem:a50338fe8ce60e175fa5a42046ea70ed0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a50338fe8ce60e175fa5a42046ea70ed0">matrix</a> ()</td></tr>
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<tr class="memitem:a5667367476f2c9a0257ae2614e5ec5ad"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a5667367476f2c9a0257ae2614e5ec5ad">matrix</a> () const</td></tr>
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<tr class="memitem:ab3fd41ce001f1a09f08593bcef075bbd"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ab3fd41ce001f1a09f08593bcef075bbd">operator()</a> (<a class="el" href="classEigen_1_1Transform.html#ae5001c5914013c18924faa92590251f6">Index</a> row, <a class="el" href="classEigen_1_1Transform.html#ae5001c5914013c18924faa92590251f6">Index</a> col)</td></tr>
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<tr class="memitem:a2cf0102f72714f18ff3bf787e4b5b5a7"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a2cf0102f72714f18ff3bf787e4b5b5a7">operator()</a> (<a class="el" href="classEigen_1_1Transform.html#ae5001c5914013c18924faa92590251f6">Index</a> row, <a class="el" href="classEigen_1_1Transform.html#ae5001c5914013c18924faa92590251f6">Index</a> col) const</td></tr>
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<tr class="memitem:a9698e25d64567157be051c1a0b7917de"><td class="memTemplParams" colspan="2">template&lt;typename DiagonalDerived &gt; </td></tr>
<tr class="memitem:a9698e25d64567157be051c1a0b7917de"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transform.html#a8a56c160574e9f4da03c987a12eefb68">TransformTimeDiagonalReturnType</a>&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a9698e25d64567157be051c1a0b7917de">operator*</a> (const DiagonalBase&lt; DiagonalDerived &gt; &amp;b) const</td></tr>
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<tr class="memitem:a8b3f4dc5db398c62d0e01f9d1741fa95"><td class="memTemplParams" colspan="2">template&lt;typename OtherDerived &gt; </td></tr>
<tr class="memitem:a8b3f4dc5db398c62d0e01f9d1741fa95"><td class="memTemplItemLeft" align="right" valign="top">const internal::transform_right_product_impl&lt; <a class="el" href="classEigen_1_1Transform.html">Transform</a>, OtherDerived &gt;::ResultType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a8b3f4dc5db398c62d0e01f9d1741fa95">operator*</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; OtherDerived &gt; &amp;other) const</td></tr>
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<tr class="memitem:a87b0a04690eb179856b6ef63f7ee1f9d"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transform.html">Transform</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a87b0a04690eb179856b6ef63f7ee1f9d">operator*</a> (const <a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;other) const</td></tr>
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<tr class="memitem:a4476f8e1255864ac287ce13bcd518356"><td class="memTemplParams" colspan="2">template&lt;int OtherMode, int OtherOptions&gt; </td></tr>
<tr class="memitem:a4476f8e1255864ac287ce13bcd518356"><td class="memTemplItemLeft" align="right" valign="top">internal::transform_transform_product_impl&lt; <a class="el" href="classEigen_1_1Transform.html">Transform</a>, <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, OtherMode, OtherOptions &gt; &gt;::ResultType&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a4476f8e1255864ac287ce13bcd518356">operator*</a> (const <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, OtherMode, OtherOptions &gt; &amp;other) const</td></tr>
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<tr class="memitem:aa9d2c3a9e3c7883621ccf723844e86da"><td class="memTemplParams" colspan="2">template&lt;typename OtherDerived &gt; </td></tr>
<tr class="memitem:aa9d2c3a9e3c7883621ccf723844e86da"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#aa9d2c3a9e3c7883621ccf723844e86da">operator=</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; OtherDerived &gt; &amp;other)</td></tr>
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<tr class="memitem:a54986164dcb1d0f7bfa216b8ef5272f6"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a54986164dcb1d0f7bfa216b8ef5272f6">operator=</a> (const QTransform &amp;other)</td></tr>
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<tr class="memitem:a7adfb258bafabe1777a0cbe4ec8997e7"><td class="memTemplParams" colspan="2">template&lt;typename RotationType &gt; </td></tr>
<tr class="memitem:a7adfb258bafabe1777a0cbe4ec8997e7"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Mode, Options &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a7adfb258bafabe1777a0cbe4ec8997e7">prerotate</a> (const RotationType &amp;<a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation</a>)</td></tr>
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<tr class="memitem:aaace811c530e5a6cc6c914a73a0cc8a4"><td class="memTemplParams" colspan="2">template&lt;typename OtherDerived &gt; </td></tr>
<tr class="memitem:aaace811c530e5a6cc6c914a73a0cc8a4"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Mode, Options &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#aaace811c530e5a6cc6c914a73a0cc8a4">prescale</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; OtherDerived &gt; &amp;other)</td></tr>
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<tr class="memitem:a96c5e49e1d779299f4975dfef93e14b3"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a96c5e49e1d779299f4975dfef93e14b3">prescale</a> (const <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &amp;s)</td></tr>
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<tr class="memitem:a17c40209cfd2d094cf654504aca95bf1"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a17c40209cfd2d094cf654504aca95bf1">preshear</a> (const <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &amp;sx, const <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &amp;sy)</td></tr>
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<tr class="memitem:a4f6cd957f1dae0799475320054823108"><td class="memTemplParams" colspan="2">template&lt;typename OtherDerived &gt; </td></tr>
<tr class="memitem:a4f6cd957f1dae0799475320054823108"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Mode, Options &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a4f6cd957f1dae0799475320054823108">pretranslate</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; OtherDerived &gt; &amp;other)</td></tr>
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<tr class="memitem:a66c55b8494d387d2e42260143ab6a385"><td class="memTemplParams" colspan="2">template&lt;typename RotationType &gt; </td></tr>
<tr class="memitem:a66c55b8494d387d2e42260143ab6a385"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Mode, Options &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a66c55b8494d387d2e42260143ab6a385">rotate</a> (const RotationType &amp;<a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation</a>)</td></tr>
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<tr class="memitem:ad73300a550f878bb7f34485c3d132746"><td class="memItemLeft" align="right" valign="top">RotationReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation</a> () const</td></tr>
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<tr class="memitem:ae4b9d6c0ed881e7fbb552550e985fd50"><td class="memTemplParams" colspan="2">template&lt;typename OtherDerived &gt; </td></tr>
<tr class="memitem:ae4b9d6c0ed881e7fbb552550e985fd50"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Mode, Options &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ae4b9d6c0ed881e7fbb552550e985fd50">scale</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; OtherDerived &gt; &amp;other)</td></tr>
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<tr class="memitem:a7757f5d9e708e625cbd936b19269b2c8"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a7757f5d9e708e625cbd936b19269b2c8">scale</a> (const <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &amp;s)</td></tr>
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<tr class="memitem:a79155e1b04e73051ae194fe62cb980fd"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a79155e1b04e73051ae194fe62cb980fd">setIdentity</a> ()</td></tr>
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<tr class="memitem:ae93a25d5e15af9446d7e5bc0e7a959d0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ae93a25d5e15af9446d7e5bc0e7a959d0">shear</a> (const <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &amp;sx, const <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a> &amp;sy)</td></tr>
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<tr class="memitem:ae954e369a06472f44b72b199beb83cd2"><td class="memItemLeft" align="right" valign="top">QTransform&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ae954e369a06472f44b72b199beb83cd2">toQTransform</a> (void) const</td></tr>
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<tr class="memitem:ae6a48c9326e794b8da277f4b15aa92d1"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ae6a48c9326e794b8da277f4b15aa92d1">Transform</a> ()</td></tr>
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<tr class="memitem:ab1e42db8cdffea634f4094d56850ab6e"><td class="memTemplParams" colspan="2">template&lt;typename OtherDerived &gt; </td></tr>
<tr class="memitem:ab1e42db8cdffea634f4094d56850ab6e"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ab1e42db8cdffea634f4094d56850ab6e">Transform</a> (const <a class="el" href="structEigen_1_1EigenBase.html">EigenBase</a>&lt; OtherDerived &gt; &amp;other)</td></tr>
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<tr class="memitem:a63e9a5b9cf964921c24023dd680dee6d"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a63e9a5b9cf964921c24023dd680dee6d">Transform</a> (const QTransform &amp;other)</td></tr>
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<tr class="memitem:aac6142c294732a1ce692799c908fa81a"><td class="memTemplParams" colspan="2">template&lt;typename OtherScalarType &gt; </td></tr>
<tr class="memitem:aac6142c294732a1ce692799c908fa81a"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#aac6142c294732a1ce692799c908fa81a">Transform</a> (const <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; OtherScalarType, Dim, Mode, Options &gt; &amp;other)</td></tr>
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<tr class="memitem:ab3d46c808fd22676aaf737c89ea4a846"><td class="memTemplParams" colspan="2">template&lt;typename OtherDerived &gt; </td></tr>
<tr class="memitem:ab3d46c808fd22676aaf737c89ea4a846"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, Mode, Options &gt; &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#ab3d46c808fd22676aaf737c89ea4a846">translate</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; OtherDerived &gt; &amp;other)</td></tr>
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<tr class="memitem:afbb1026d0b81b51fea103bd8fc947f57"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#a98ad9f68ecea39c6f0b5fcf184fbcb47">TranslationPart</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#afbb1026d0b81b51fea103bd8fc947f57">translation</a> ()</td></tr>
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<tr class="memitem:a539fc3e91b20a43613bfefb8a4fb8a0e"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1Transform.html#ae0f9a88eecc888dbffb8b27f67d2e540">ConstTranslationPart</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a539fc3e91b20a43613bfefb8a4fb8a0e">translation</a> () const</td></tr>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-methods"></a>
Static Public Member Functions</h2></td></tr>
<tr class="memitem:a15ba7101d08163b421ab439c90721524"><td class="memItemLeft" align="right" valign="top">static const <a class="el" href="classEigen_1_1Transform.html">Transform</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1Transform.html#a15ba7101d08163b421ab439c90721524">Identity</a> ()</td></tr>
<tr class="memdesc:a15ba7101d08163b421ab439c90721524"><td class="mdescLeft">&#160;</td><td class="mdescRight">Returns an identity transformation.  <a href="classEigen_1_1Transform.html#a15ba7101d08163b421ab439c90721524">More...</a><br /></td></tr>
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<h2 class="groupheader">Member Typedef Documentation</h2>
<a id="aa4d22f6827bf7c2b67d0c609c8e31fdb"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa4d22f6827bf7c2b67d0c609c8e31fdb">&#9670;&nbsp;</a></span>AffinePart</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef std::conditional_t&lt;int(Mode)==int(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>), <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>&amp;, <a class="el" href="classEigen_1_1Block.html">Block</a>&lt;<a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>,Dim,HDim&gt; &gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#aa4d22f6827bf7c2b67d0c609c8e31fdb">AffinePart</a></td>
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<p>type of read/write reference to the affine part of the transformation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a0919aff2b16c0c97cbfa4dd16a71c946">&#9670;&nbsp;</a></span>ConstAffinePart</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef std::conditional_t&lt;int(Mode)==int(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>), const <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>&amp;, const <a class="el" href="classEigen_1_1Block.html">Block</a>&lt;const <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>,Dim,HDim&gt; &gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#a0919aff2b16c0c97cbfa4dd16a71c946">ConstAffinePart</a></td>
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<p>type of read reference to the affine part of the transformation </p>

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<a id="a9ebace9975ee01a2b82f63ee353a549a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9ebace9975ee01a2b82f63ee353a549a">&#9670;&nbsp;</a></span>ConstLinearPart</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef const <a class="el" href="classEigen_1_1Block.html">Block</a>&lt;<a class="el" href="classEigen_1_1Transform.html#ada1f35e4ec62a77c63c99282f95cbbc8">ConstMatrixType</a>,Dim,Dim,int(Mode)==(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>) &amp;&amp; (int(Options)&amp;<a class="el" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>)==0&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#a9ebace9975ee01a2b82f63ee353a549a">ConstLinearPart</a></td>
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<p>type of read reference to the linear part of the transformation </p>

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<a id="ada1f35e4ec62a77c63c99282f95cbbc8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ada1f35e4ec62a77c63c99282f95cbbc8">&#9670;&nbsp;</a></span>ConstMatrixType</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef const <a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a> <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#ada1f35e4ec62a77c63c99282f95cbbc8">ConstMatrixType</a></td>
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<p>constified MatrixType </p>

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<a id="ae0f9a88eecc888dbffb8b27f67d2e540"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae0f9a88eecc888dbffb8b27f67d2e540">&#9670;&nbsp;</a></span>ConstTranslationPart</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef const <a class="el" href="classEigen_1_1Block.html">Block</a>&lt;<a class="el" href="classEigen_1_1Transform.html#ada1f35e4ec62a77c63c99282f95cbbc8">ConstMatrixType</a>,Dim,1,!(internal::traits&lt;<a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>&gt;::Flags &amp; <a class="el" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a>)&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#ae0f9a88eecc888dbffb8b27f67d2e540">ConstTranslationPart</a></td>
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<p>type of a read reference to the translation part of the rotation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ae5001c5914013c18924faa92590251f6">&#9670;&nbsp;</a></span>Index</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a> <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#ae5001c5914013c18924faa92590251f6">Index</a></td>
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<dl class="deprecated"><dt><b><a class="el" href="deprecated.html#_deprecated000031">Deprecated:</a></b></dt><dd>since <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> 3.3 </dd></dl>

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<a id="ae14a5178e9c3b434b6ab343bba8a9232"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae14a5178e9c3b434b6ab343bba8a9232">&#9670;&nbsp;</a></span>LinearMatrixType</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt;<a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>,Dim,Dim,Options&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#ae14a5178e9c3b434b6ab343bba8a9232">LinearMatrixType</a></td>
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<p>type of the matrix used to represent the linear part of the transformation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ad6d84e2c0438b13fc4fff332aca116fa">&#9670;&nbsp;</a></span>LinearPart</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef <a class="el" href="classEigen_1_1Block.html">Block</a>&lt;<a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>,Dim,Dim,int(Mode)==(<a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a8192e8fdb2ec3ec46d92956cc83ef490">AffineCompact</a>) &amp;&amp; (int(Options)&amp;<a class="el" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>)==0&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#ad6d84e2c0438b13fc4fff332aca116fa">LinearPart</a></td>
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<p>type of read/write reference to the linear part of the transformation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a2c59f34fa172d9781f1bdd18d83e6c23">&#9670;&nbsp;</a></span>MatrixType</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef internal::make_proper_matrix_type&lt;<a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>,Rows,HDim,Options&gt;::type <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a></td>
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<p>type of the matrix used to represent the transformation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a37f6f58b51298ca64c6cf8457a73538d">&#9670;&nbsp;</a></span>Scalar</h2>

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          <td class="memname">typedef Scalar_ <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a></td>
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<p>the scalar type of the coefficients </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a8a56c160574e9f4da03c987a12eefb68">&#9670;&nbsp;</a></span>TransformTimeDiagonalReturnType</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt;<a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>,Dim,TransformTimeDiagonalMode&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#a8a56c160574e9f4da03c987a12eefb68">TransformTimeDiagonalReturnType</a></td>
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<p>The return type of the product between a diagonal matrix and a transform </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a98ad9f68ecea39c6f0b5fcf184fbcb47">&#9670;&nbsp;</a></span>TranslationPart</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef <a class="el" href="classEigen_1_1Block.html">Block</a>&lt;<a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>,Dim,1,!(internal::traits&lt;<a class="el" href="classEigen_1_1Transform.html#a2c59f34fa172d9781f1bdd18d83e6c23">MatrixType</a>&gt;::Flags &amp; <a class="el" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a>)&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#a98ad9f68ecea39c6f0b5fcf184fbcb47">TranslationPart</a></td>
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<p>type of a read/write reference to the translation part of the rotation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#af0ce638b81842cd4622f67d5ab655b2e">&#9670;&nbsp;</a></span>TranslationType</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef <a class="el" href="classEigen_1_1Translation.html">Translation</a>&lt;<a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>,Dim&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#af0ce638b81842cd4622f67d5ab655b2e">TranslationType</a></td>
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<p>corresponding translation type </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a7b27e078095260aebef444023b96d090">&#9670;&nbsp;</a></span>VectorType</h2>

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template&lt;typename Scalar_ , int Dim_, int Mode_, int Options_&gt; </div>
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          <td class="memname">typedef <a class="el" href="classEigen_1_1Matrix.html">Matrix</a>&lt;<a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>,Dim,1&gt; <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::<a class="el" href="classEigen_1_1Transform.html#a7b27e078095260aebef444023b96d090">VectorType</a></td>
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<p>type of a vector </p>

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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae6a48c9326e794b8da277f4b15aa92d1">&#9670;&nbsp;</a></span>Transform() <span class="overload">[1/4]</span></h2>

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<p>Default constructor without initialization of the meaningful coefficients. If Mode==Affine or Mode==Isometry, then the last row is set to [0 ... 0 1] </p>

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<p>Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. </p>

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<p>Initializes <code>*this</code> from a QTransform assuming the dimension is 2.</p>
<p>This function is available only if the token EIGEN_QT_SUPPORT is defined. </p>

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<p>Copy constructor with scalar type conversion </p>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a61b7a97da2ce3e46902d97af27c1a79a">&#9670;&nbsp;</a></span>affine() <span class="overload">[1/2]</span></h2>

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<dl class="section return"><dt>Returns</dt><dd>a writable expression of the Dim x HDim affine part of the transformation </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>a read-only expression of the Dim x HDim affine part of the transformation </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a3ed6d91135a87d168d5470a51f1dbb3b">&#9670;&nbsp;</a></span>cast()</h2>

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<dl class="section return"><dt>Returns</dt><dd><code>*this</code> with scalar type casted to <em>NewScalarType</em> </dd></dl>
<p>Note that if <em>NewScalarType</em> is equal to the current scalar type of <code>*this</code> then this function smartly returns a const reference to <code>*this</code>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a7213fd78501c1185c4a1441e33c812d3">&#9670;&nbsp;</a></span>computeRotationScaling()</h2>

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<p>decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive.</p>
<p>If either pointer is zero, the corresponding computation is skipped.</p>
<p>This is defined in the SVD module.</p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/SVD&gt;</span> </div>
</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1Transform.html#a247b079c63f46bb652b3776484838216">computeScalingRotation()</a>, <a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation()</a>, class SVD </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a247b079c63f46bb652b3776484838216">&#9670;&nbsp;</a></span>computeScalingRotation()</h2>

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<p>decomposes the linear part of the transformation as a product scaling x rotation, the scaling being not necessarily positive.</p>
<p>If either pointer is zero, the corresponding computation is skipped.</p>
<p>This is defined in the SVD module.</p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/SVD&gt;</span> </div>
</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1Transform.html#a7213fd78501c1185c4a1441e33c812d3">computeRotationScaling()</a>, <a class="el" href="classEigen_1_1Transform.html#ad73300a550f878bb7f34485c3d132746">rotation()</a>, class SVD </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>a non-const pointer to the column major internal matrix </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>a const pointer to the column major internal matrix </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a7924a893752f42d33ca8dca33280ebc7">&#9670;&nbsp;</a></span>EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE()</h2>

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<p>&lt; space dimension in which the transformation holds</p>
<p>&lt; size of a respective homogeneous vector</p>

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<h2 class="memtitle"><span class="permalink"><a href="#a4fbbe0434e3093ec44287f45f27b66e3">&#9670;&nbsp;</a></span>fromPositionOrientationScale()</h2>

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<p>Convenient method to set <code>*this</code> from a position, orientation and scale of a 3D object. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a15ba7101d08163b421ab439c90721524">&#9670;&nbsp;</a></span>Identity()</h2>

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<p>Returns an identity transformation. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ab8dbcd157bf194efca1a5413c0945211">&#9670;&nbsp;</a></span>inverse()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the inverse transformation according to some given knowledge on <code>*this</code>.</dd></dl>
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<li><a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a0f7338b8672884554e8642bce9e44183">Projective</a> if the transformation is not necessarily affine, i.e., if the last row is not guaranteed to be [0 ... 0 1]</li>
<li><a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a0872f0a82453aaae40339c33acbb31fb">Affine</a> if the last row can be assumed to be [0 ... 0 1]</li>
<li><a class="el" href="group__enums.html#ggaee59a86102f150923b0cac6d4ff05107a84413028615d2d718bafd2dfb93dafef">Isometry</a> if the transformation is only a concatenations of translations and rotations. The default is the template class parameter <code>Mode</code>.</li>
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<dl class="section warning"><dt>Warning</dt><dd>unless <em>traits</em> is always set to NoShear or NoScaling, this function requires the generic inverse method of <a class="el" href="classEigen_1_1MatrixBase.html" title="Base class for all dense matrices, vectors, and expressions.">MatrixBase</a> defined in the LU module. If you forget to include this module, then you will get hard to debug linking errors.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a7712eb69e8ea3c8f7b8da1c44dbdeebf">MatrixBase::inverse()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a5ca48af274337349e9b8d129ecf7c35b">&#9670;&nbsp;</a></span>isApprox()</h2>

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<dl class="section return"><dt>Returns</dt><dd><code>true</code> if <code>*this</code> is approximately equal to <em>other</em>, within the precision determined by <em>prec</em>.</dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1DenseBase.html#ae8443357b808cd393be1b51974213f9c">MatrixBase::isApprox()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a8aafb7e536e68b13b05a5cbd24d71379">&#9670;&nbsp;</a></span>linear() <span class="overload">[1/2]</span></h2>

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<dl class="section return"><dt>Returns</dt><dd>a writable expression of the linear part of the transformation </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>a read-only expression of the linear part of the transformation </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#adb282510aef3951e1deb27466cf8167b">&#9670;&nbsp;</a></span>makeAffine()</h2>

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<p>Sets the last row to [0 ... 0 1] </p>

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<dl class="section return"><dt>Returns</dt><dd>a writable expression of the transformation matrix </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>a read-only expression of the transformation matrix </dd></dl>

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<p>shortcut for m_matrix(row,col); </p><dl class="section see"><dt>See also</dt><dd>MatrixBase::operator(Index,Index) </dd></dl>

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<p>shortcut for m_matrix(row,col); </p><dl class="section see"><dt>See also</dt><dd>MatrixBase::operator(Index,Index) const  </dd></dl>

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<dl class="section return"><dt>Returns</dt><dd>The product expression of a transform <em>a</em> times a diagonal matrix <em>b</em> </dd></dl>
<p>The rhs diagonal matrix is interpreted as an affine scaling transformation. The product results in a <a class="el" href="classEigen_1_1Transform.html" title="Represents an homogeneous transformation in a N dimensional space.">Transform</a> of the same type (mode) as the lhs only if the lhs mode is no isometry. In that case, the returned transform is an affinity. </p>

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<dl class="section return"><dt>Returns</dt><dd>an expression of the product between the transform <code>*this</code> and a matrix expression <em>other</em>.</dd></dl>
<p>The right-hand-side <em>other</em> can be either: </p><ul>
<li>an homogeneous vector of size Dim+1, </li>
<li>a set of homogeneous vectors of size Dim+1 x N, </li>
<li>a transformation matrix of size Dim+1 x Dim+1.</li>
</ul>
<p>Moreover, if <code>*this</code> represents an affine transformation (i.e., Mode!=Projective), then <em>other</em> can also be: </p><ul>
<li>a point of size Dim (computes:<div class="fragment"><div class="line">this-&gt;<a class="code" href="classEigen_1_1Transform.html#a10681d9bbc6a7a81a9111b1f9e186948">linear</a>() * other + this-&gt;<a class="code" href="classEigen_1_1Transform.html#a539fc3e91b20a43613bfefb8a4fb8a0e">translation</a>()</div>
<div class="ttc" id="aclassEigen_1_1Transform_html_a10681d9bbc6a7a81a9111b1f9e186948"><div class="ttname"><a href="classEigen_1_1Transform.html#a10681d9bbc6a7a81a9111b1f9e186948">Eigen::Transform::linear</a></div><div class="ttdeci">ConstLinearPart linear() const</div><div class="ttdef"><b>Definition:</b> Transform.h:398</div></div>
<div class="ttc" id="aclassEigen_1_1Transform_html_a539fc3e91b20a43613bfefb8a4fb8a0e"><div class="ttname"><a href="classEigen_1_1Transform.html#a539fc3e91b20a43613bfefb8a4fb8a0e">Eigen::Transform::translation</a></div><div class="ttdeci">ConstTranslationPart translation() const</div><div class="ttdef"><b>Definition:</b> Transform.h:408</div></div>
</div><!-- fragment -->), </li>
<li>a set of N points as a Dim x N matrix (computes:<div class="fragment"><div class="line">(this-&gt;<a class="code" href="classEigen_1_1Transform.html#a10681d9bbc6a7a81a9111b1f9e186948">linear</a>() * other).colwise() + this-&gt;<a class="code" href="classEigen_1_1Transform.html#a539fc3e91b20a43613bfefb8a4fb8a0e">translation</a>()</div>
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<p>In all cases, the return type is a matrix or vector of same sizes as the right-hand-side <em>other</em>.</p>
<p>If you want to interpret <em>other</em> as a linear or affine transformation, then first convert it to a Transform&lt;&gt; type, or do your own cooking.</p>
<p>Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only: </p><div class="fragment"><div class="line">Affine3f A;</div>
<div class="line"><a class="code" href="group__matrixtypedefs.html#ga5ec9ce2d8adbcd6888f3fbf2e1c095a4">Vector3f</a> v1, v2;</div>
<div class="line">v2 = A.linear() * v1;</div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga5ec9ce2d8adbcd6888f3fbf2e1c095a4"><div class="ttname"><a href="group__matrixtypedefs.html#ga5ec9ce2d8adbcd6888f3fbf2e1c095a4">Eigen::Vector3f</a></div><div class="ttdeci">Matrix&lt; float, 3, 1 &gt; Vector3f</div><div class="ttdoc">3×1 vector of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
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<p>Concatenates two transformations </p>

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          <td class="paramtype">const <a class="el" href="classEigen_1_1Transform.html">Transform</a>&lt; <a class="el" href="classEigen_1_1Transform.html#a37f6f58b51298ca64c6cf8457a73538d">Scalar</a>, Dim, OtherMode, OtherOptions &gt; &amp;&#160;</td>
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<p>Concatenates two different transformations </p>

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<p>Set <code>*this</code> from a Dim^2 or (Dim+1)^2 matrix. </p>

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<p>Set <code>*this</code> from a QTransform assuming the dimension is 2.</p>
<p>This function is available only if the token EIGEN_QT_SUPPORT is defined. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a7adfb258bafabe1777a0cbe4ec8997e7">&#9670;&nbsp;</a></span>prerotate()</h2>

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<p>Applies on the left the rotation represented by the rotation <em>rotation</em> to <code>*this</code> and returns a reference to <code>*this</code>.</p>
<p>See rotate() for further details.</p>
<dl class="section see"><dt>See also</dt><dd>rotate() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#aaace811c530e5a6cc6c914a73a0cc8a4">&#9670;&nbsp;</a></span>prescale() <span class="overload">[1/2]</span></h2>

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<p>Applies on the left the non uniform scale transformation represented by the vector <em>other</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section see"><dt>See also</dt><dd>scale() </dd></dl>

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<p>Applies on the left a uniform scale of a factor <em>c</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section see"><dt>See also</dt><dd>scale(Scalar) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a17c40209cfd2d094cf654504aca95bf1">&#9670;&nbsp;</a></span>preshear()</h2>

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<p>Applies on the left the shear transformation represented by the vector <em>other</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section warning"><dt>Warning</dt><dd>2D only. </dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1Transform.html#ae93a25d5e15af9446d7e5bc0e7a959d0">shear()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a4f6cd957f1dae0799475320054823108">&#9670;&nbsp;</a></span>pretranslate()</h2>

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<p>Applies on the left the translation matrix represented by the vector <em>other</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section see"><dt>See also</dt><dd>translate() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a66c55b8494d387d2e42260143ab6a385">&#9670;&nbsp;</a></span>rotate()</h2>

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<p>Applies on the right the rotation represented by the rotation <em>rotation</em> to <code>*this</code> and returns a reference to <code>*this</code>.</p>
<p>The template parameter <em>RotationType</em> is the type of the rotation which must be known by internal::toRotationMatrix&lt;&gt;.</p>
<p>Natively supported types includes:</p><ul>
<li>any scalar (2D),</li>
<li>a Dim x Dim matrix expression,</li>
<li>a <a class="el" href="classEigen_1_1Quaternion.html" title="The quaternion class used to represent 3D orientations and rotations.">Quaternion</a> (3D),</li>
<li>a <a class="el" href="classEigen_1_1AngleAxis.html" title="Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.">AngleAxis</a> (3D)</li>
</ul>
<p>This mechanism is easily extendable to support user types such as Euler angles, or a pair of <a class="el" href="classEigen_1_1Quaternion.html" title="The quaternion class used to represent 3D orientations and rotations.">Quaternion</a> for 4D rotations.</p>
<dl class="section see"><dt>See also</dt><dd>rotate(Scalar), class <a class="el" href="classEigen_1_1Quaternion.html" title="The quaternion class used to represent 3D orientations and rotations.">Quaternion</a>, class <a class="el" href="classEigen_1_1AngleAxis.html" title="Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.">AngleAxis</a>, prerotate(RotationType) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ad73300a550f878bb7f34485c3d132746">&#9670;&nbsp;</a></span>rotation()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the rotation part of the transformation</dd></dl>
<p>If Mode==Isometry, then this method is an alias for <a class="el" href="classEigen_1_1Transform.html#a8aafb7e536e68b13b05a5cbd24d71379">linear()</a>, otherwise it calls <a class="el" href="classEigen_1_1Transform.html#a7213fd78501c1185c4a1441e33c812d3">computeRotationScaling()</a> to extract the rotation through a SVD decomposition.</p>
<p>This is defined in the SVD module.</p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/SVD&gt;</span> </div>
</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1Transform.html#a7213fd78501c1185c4a1441e33c812d3">computeRotationScaling()</a>, <a class="el" href="classEigen_1_1Transform.html#a247b079c63f46bb652b3776484838216">computeScalingRotation()</a>, class SVD </dd></dl>

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<p>Applies on the right the non uniform scale transformation represented by the vector <em>other</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section see"><dt>See also</dt><dd>prescale() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a7757f5d9e708e625cbd936b19269b2c8">&#9670;&nbsp;</a></span>scale() <span class="overload">[2/2]</span></h2>

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<p>Applies on the right a uniform scale of a factor <em>c</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section see"><dt>See also</dt><dd>prescale(Scalar) </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a79155e1b04e73051ae194fe62cb980fd">&#9670;&nbsp;</a></span>setIdentity()</h2>

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<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a18e969adfdf2db4ac44c47fbdc854683">MatrixBase::setIdentity()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ae93a25d5e15af9446d7e5bc0e7a959d0">&#9670;&nbsp;</a></span>shear()</h2>

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<p>Applies on the right the shear transformation represented by the vector <em>other</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section warning"><dt>Warning</dt><dd>2D only. </dd></dl>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1Transform.html#a17c40209cfd2d094cf654504aca95bf1">preshear()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ae954e369a06472f44b72b199beb83cd2">&#9670;&nbsp;</a></span>toQTransform()</h2>

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<dl class="section return"><dt>Returns</dt><dd>a QTransform from <code>*this</code> assuming the dimension is 2.</dd></dl>
<p>This function is available only if the token EIGEN_QT_SUPPORT is defined. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ab3d46c808fd22676aaf737c89ea4a846">&#9670;&nbsp;</a></span>translate()</h2>

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<p>Applies on the right the translation matrix represented by the vector <em>other</em> to <code>*this</code> and returns a reference to <code>*this</code>. </p><dl class="section see"><dt>See also</dt><dd>pretranslate() </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#afbb1026d0b81b51fea103bd8fc947f57">&#9670;&nbsp;</a></span>translation() <span class="overload">[1/2]</span></h2>

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<dl class="section return"><dt>Returns</dt><dd>a writable expression of the translation vector of the transformation </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a539fc3e91b20a43613bfefb8a4fb8a0e">&#9670;&nbsp;</a></span>translation() <span class="overload">[2/2]</span></h2>

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          <td class="memname"><a class="el" href="classEigen_1_1Transform.html#ae0f9a88eecc888dbffb8b27f67d2e540">ConstTranslationPart</a> <a class="el" href="classEigen_1_1Transform.html">Eigen::Transform</a>&lt; Scalar_, Dim_, Mode_, Options_ &gt;::translation </td>
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<dl class="section return"><dt>Returns</dt><dd>a read-only expression of the translation vector of the transformation </dd></dl>

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